Reduction of fouling in high pressure reactors

ABSTRACT

The Application of equations of state to experimental and literature data permits the formation of a model and phase diagram(s) that show under what conditions polyethylene is likely to precipitate out of a high pressure solution of polyethylene in supercritical ethylene. This then permits a better definition to run a high pressure reactor to reduce the likelihood of phase separation, loss of cooling and potentially decomposition of the reactor contents.

REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.14/078,576 filed on Nov. 13, 2013 entitled “Reduction of Fouling In HighPressure Reactors”, now issued as U.S. Pat. No. 9,202,014, which claimsforeign priority to Canada 2798036 filed Dec. 5, 2012, which is hereinincorporated by reference in its entirety.

FIELD OF THE INVENTION

The present invention relates to the field of high pressurepolymerization of alpha olefins, and, for example, ethylene and co- andhomo-polymers thereof. For example, the present invention relates to theprocess for the polymerization in tubular reactors at high temperaturesand pressures.

BACKGROUND OF THE INVENTION

U.S. Pat. No. 2,153,553 issued Apr. 11, 1939 discloses the high pressurepolymerization of ethylene. The patent sets forth four conditions thatmust be met for the polymerization of ethylene to solid polymers. Thepressure should be above 500 atmospheres, the temperature should bebetween 100 and 400° C. The oxygen content of the reactants must notexceed a very small critical amount, and there must be sufficientthermal control of the reaction to avoid undue rise in temperature. Thepatent then contains a caution. If the four conditions are not properlymet there is either no reaction or there is an undesired reaction ofexplosive violence giving rise to carbon and methane. The latter issometimes euphemistically referred to as a “decomp”.

During polymerization it has been observed that there may be a periodwhere heat transfer from the reaction to the cooling jacket is impaired.Given the warning above it is imperative to either not impair thecooling capacity or to quickly restore the cooling capacity of thecooling jacket if it is impaired. It is believed that this loss ofcooling efficiency is caused by deposition of polymer on the internalreactor wall. The current methods of removing polymer deposits from theinternal reactor wall are primarily physical (i.e. send a pressureshockwave along the tube to dislodge any polymer residue).

Additionally, some operators may cycle the jacket temperatures fromnormal set points to about 150-200° C. for a several hours, in anattempt to dissolve or shed polymer deposits on the internal walls ofthe reactor.

In the operation of a high pressure polyethylene plant there are anumber of conflicting desiderata. To achieve highest conversion one mayset a high difference in temperature between the reactants and thecooling medium in the reactor shell (jacket) temperature. On the otherhand, one may want to know at what temperatures polymer is likely toprecipitate on the internal wall of the reactor leading to a number ofpotential consequences including reactor wall fouling, loss of cooling,formation of gels and ultimately a decomposition of the contents of thereactor.

SUMMARY OF THE INVENTION

In one embodiment, the invention provides a method to determine theliquid liquid equilibrium boundary and the critical polymerconcentration as a function of molecular weight distribution (MWD) for amultitude of different products comprising from about 80 to about 100wt. % of ethylene and about 0 up to about 20 weight % of one or moreC₃₋₈ alpha olefins having a weight average molecular weight from about8,000 to about 500,000 (which includes a minor component having amolecular weight of about 500,000 or greater) produced in super criticalethylene in a high pressure reactor at temperatures from about 80° C. toabout 350° C. and pressures from about 100 MPa to about 350 MPacomprising:

-   -   1—modeling experimental or literature data for the liquid liquid        equilibrium using an equation of state model (for example, the        Sanchez-Lacombe or the perturbed chain statistical associating        fluid theory equation of state to describe the effects of the        molecular weight and the polydispersity of the polyethylene on        the liquid liquid equilibrium curve    -   2—determining the composition-specific parameters of the model        from 1; and    -   3—applying the resultant equation of state model to the        temperature, pressure and composition conditions of the reaction        to generate the liquid liquid equilibrium boundary and        optionally the critical polymer concentration (as used herein        “the critical polymer concentration” means the point below which        droplets of a phase with a higher concentration in polymer are        formed and above which droplets primarily of solvent (i.e.        ethylene) are formed).

In a further embodiment the reactor is a tubular reactor.

In a further embodiment there is provided a method to prepare a liquidpolymer lean/liquid polymer rich and liquid liquid phase diagram for areactor for polymerizing a system comprising a polymer having a weightaverage molecular weight from about 8,000 to about 500,000 comprisingfrom about 80 to about 100 wt % of ethylene and about 0 to about 20 wt %of one or more C₃₋₈ alpha olefins in super critical liquid ethylene attemperatures from about 80° C. to about 350° C. and pressures from about100 MPa to about 350 MPa to define operating conditions at which thepolymer is substantially dissolved in the liquid phase comprising:

a) preparing a phase diagram for liquid polymer lean/liquid polymer richfor said reactor and process at temperatures from about 150° C. to about350° C. and pressures from about 100 to about 350 MPa;

b) inserting into said phase diagram a liquid liquid phase boundarydetermined as above.

As used herein the polymer is substantially dissolved in the liquidphase if great than about 90% of the polymer is dissolved in the liquidphase. In another embodiment, greater than about 95% of the polymer maybe dissolved in the liquid phase. In another embodiment, greater thanabout 98% of the polymer may be dissolved in the liquid phase. Inanother embodiment, greater than about 99% of the polymer may bedissolved in the liquid phase. In another embodiment, 100% of thepolymer may be dissolved in the liquid phase.

In a further embodiment there is provided a method for conducting thepolymerization of a polymer having a weight average molecular weightfrom about 8,000 to about 500,000 comprising about 80 to about 100 wt %of ethylene and about 0 to about 20 wt % of one or more C₃₋₈ alphaolefins in super critical liquid ethylene at temperatures from about 80°C. to about 350° C. and pressures from about 100 MPa to about 350 MPa todefine operating conditions at which the polymer is substantiallydissolved in the liquid phase comprising monitoring the heat balance ofsaid reaction and determining when there is an apparent loss of coolingand comparing the operating conditions to the above phase diagram andadjusting one or more of the temperature and pressure conditions tobring the operating conditions more than about 5% within the liquid areaof the phase diagram.

In a further embodiment the operating conditions are adjusted to bringthem within the liquid area of the phase diagram by more than about 10%.

In a further embodiment the phase diagram is digitized and stored on amicroprocessor and heat balance for the reaction is monitored using amicroprocessor and the operating conditions are adjusted using amicroprocessor.

In a further embodiment there is provided a method to extend the runtime between cleanings of a high pressures reactor for thepolymerization of the polymerization of a polymer having a weightaverage molecular weight from about 8,000 to about 500,000 comprisingabout 80 to about 100 wt % of ethylene and about 0 to about 20 wt % ofone or more C₃₋₈ alpha olefins in super critical ethylene attemperatures from about 80° C. to about 350° C. and pressures from about100 MPa to about 350 MPa comprising operating as described above, sothat not more than about 30 minutes elapse between the apparent loss ofcooling and achieving the new operating conditions within the liquidarea within the phase diagram.

In a further embodiment the time to achieve the adjusted operatingconditions is less than about 15 minutes.

In a further embodiment there is provided a method to dissolveprecipitated polymer in a high pressures reactor for the polymerizationof the polymerization of a polymer having a weight average molecularweight from about 8,000 to about 500,000 comprising about 80 to about100 wt % of ethylene and about 0 to about 20 wt % of one or more C₃₋₈alpha olefins in super critical liquid ethylene at temperatures fromabout 80° C. to about 350° C. and pressures from about 100 MPa to about350 MPa comprising operating as outlined above, so that not more thanabout 30 minutes elapse between the apparent loss of cooling andachieving the new operating conditions within the liquid area within thephase diagram.

In a further embodiment the phase diagram is digitized and stored on amicroprocessor and heat balance for the reaction is monitored using amicroprocessor and the operating conditions are adjusted using amicroprocessor.

In a further embodiment the time to achieve the adjusted operatingconditions is less than about 15 minutes.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a calculated plot of the effect of molecular weight on theisobaric phase diagram for the ethylene-polyethylene system at 210 MPa,based on the Sanchez-Lacombe equation of state with monodispersepolymer. In FIG. 1 the area above a plot is a single phase region whilethe area below a plot is a two phase region.

FIG. 2 is a calculated plot of the isobaric liquid-liquid phaseboundaries (cloud point curves) for four commercial polyethylenes at 210MPa, based on the Sanchez-Lacombe equation of state.

FIG. 3 is a calculated plot of the isobaric liquid-liquid phase boundaryfor commercial polyethylene LFY320C as a function of pressure, based onthe Sanchez-Lacombe equation of state.

FIG. 4 is a calculated plot of the isobaric cloud point curve overlaidwith a curve showing the magnitude of the weight-average molecularweight of polymer in the new phase formed at the cloud point. forcommercial polyethylene LFY320C, based on the Sanchez-Lacombe equationof state.

FIG. 5 shows the crystallization temperature of solutions ofpolyethylene in isohexane under shear.

FIG. 6 is a schematic diagram of dispersion interactions of two n-alkanechains of covalently bonded spheres based on an averaged radialdistribution function showing reaction between indistinguishablesegments of the chains.

FIG. 7 is diagram of the inter-segment potential energy function used inthe PC-SAFT equation of state.

FIG. 8 is a calculated plot of cloud point (temperature of phaseseparation) as a function of polymer concentration for various molecularweights of polyethylene in an ethylene solution at a pressure of 200MPa.

DETAILED DESCRIPTION

Other than in the operating examples or where otherwise indicated, allnumbers or expressions referring to quantities of ingredients, reactionconditions, etc. used in the specification and claims are to beunderstood as modified in all instances by the term “about.”Accordingly, unless indicated to the contrary, the numerical parametersset forth in the following specification and attached claims areapproximations that can vary depending upon the desired properties,which the present invention desires to obtain. At the very least, andnot as an attempt to limit the application of the doctrine ofequivalents to the scope of the claims, each numerical parameter shouldat least be construed in light of the number of reported significantdigits and by applying ordinary rounding techniques.

Notwithstanding that the numerical ranges and parameters setting forththe broad scope of the invention are approximations, the numericalvalues set forth in the examples are reported as precisely as possible.Any numerical values, however, inherently contain certain errorsnecessarily resulting from the standard deviation found in theirrespective testing measurements.

Also, it should be understood that any numerical range recited herein isintended to include all sub-ranges subsumed therein. For example, arange of “1 to 10” is intended to include all sub-ranges between andincluding the recited minimum value of 1 and the recited maximum valueof 10; that is, having a minimum value equal to or greater than 1 and amaximum value of equal to or less than 10. Because the disclosednumerical ranges are continuous, they include every value between theminimum and maximum values. Unless expressly indicated otherwise, thevarious numerical ranges specified in this application areapproximations.

All compositional ranges expressed herein are limited in total to and donot exceed 100 percent (volume percent or weight percent) in practice.Where multiple components can be present in a composition, the sum ofthe maximum amounts of each component can exceed 100 percent, with theunderstanding that, and as those skilled in the art readily understand,that the amounts of the components actually used will conform to themaximum of 100 percent.

In one embodiment, the present invention is directed to temperature andpressures regimes at which droplets of high molecular weight polymer(that is weight average molecular weight of about 500,000 or greater)may separate from the polymer solution. The polymer may precipitate onto the inner surface of the reactor walls. This may result in a numberof issues. For example, the run time between reactor cleanings may beshortened. Product quality may be impaired due to contamination bydeposited polymer coming off the reactor wall. There may also be a“decomp”.

In one embodiment, the present invention seeks to provide a method togenerate a liquid liquid equilibrium curve for high pressurepolyethylene and its homologues.

Once the liquid liquid equilibrium curve is generated it will beunderstood that phase separation and conversion are integrally related.One may operate the reactor at a wall temperature of 130° C.±5° C. in aportion of the first reaction zone, that is, at low conversions (lowpolymer concentrations) to prevent liquid liquid phase separation. Theneed to keep the reactor contents hot is governed by the criticalpolymer concentration; beyond that critical point, droplets composed ofsubstantially only ethylene, i.e. with minimal amounts of polymer, formin a continuous polymer solution phase. These solvent droplets will notlead to fouling of the inner surface of the internal reactor wall, andmay act to improve heat transfer.

In one embodiment, the present invention relates to the production ofhigh pressure, low density polyethylene (LDPE). The polyethylenecomprises from about 100 to about 80 weight %, or from about 100 toabout 90 wt. %, or from about 100 to about 95 wt. % of ethylene and fromabout 0 to about 20 wt. %, or about 0 to about 10 wt. %, or from about 0to about 5 wt. % of one or more monomers selected from C₃₋₈. In anotherembodiment the one or more monomers are selected from C₃₋₄ alphaolefins. In one embodiment the alpha olefins include propylene, butene,hexene and octene. In another embodiment, the olefins include propyleneand butene.

Although the process has been modified over time it essentiallycomprises compressing ethylene to a high enough pressure so that itbecomes a supercritical fluid. The pressures range from about 100 toabout 350 MPa (e.g., about 14,500 to about 50,800 psi) or from about 200to about 300 MPa (about 29,000 psi to about 43,500 psi) and thetemperature ranges from about 80° C. to about 350° C., or from about150° C. to about 325° C. The supercritical ethylene together with one ormore of initiators, chain transfer agent and optional comonomers are fedto a high pressure reactor. The reactor may be an autoclave reactor orfor example, a tubular reactor. Tubular reactors may have a length fromabout 200 m to about 2500 m, and a diameter from about 20 mm to about100 mm.

Thermocouples along the length of the reactor may be spaced at adistance from about 5 to about 15, or about 8 to about 12, or from about8 to about 11 meters. In some embodiments there may be from about 100and about 350 thermocouples, or from about 120 to about 300thermocouples spaced along the length of the reactor. The spacing of thethermocouples may be uniform along the length of the reactor. In someembodiments the spacing of the thermocouples may not be uniform alongthe length of the reactor.

Generally there are a number of injection points spaced along thetubular reactor where additional components such as initiators, chaintransfer agents, and monomers (for example cold monomers), may be addedto the reactor. The design and operation of tubular reactors isillustrated by a number of patents including for example U.S. Pat. No.3,334,081 issued Aug. 1, 1967 to Madgwick et al, assigned to UnionCarbide Corporation; U.S. Pat. No. 3,399,185 Issued Aug. 27, 1968 toSchappert assigned to Koppers Company, Inc., U.S. Pat. No. 3,917,577issued Nov. 4, 1975 to Trieschmann et al. assigned to Badische Anilin &Soda-Fabrik Aktiengesellschaft; and U.S. Pat. No. 4,135,044 issued Jan.16, 1979 to Beals assigned to Exxon Research & Engineering Co.

There may be a number of injection points for a high pressurepolyethylene reactor. However, as will be discussed below the issue isnot injection points. Rather the issue is conversion. As shown in FIG. 1the phase separation temperature for monodisperse polyethylene fromreactants (liquid ethylene) at pressures of about 210 MPa increases withpolymer concentration to about 115° C., at a polymer concentration ofabout 1 wt %, for a polymer having a molecular weight greater than about1,000.000. Thereafter the phase separation temperature falls. The abovetemperature is derived from a theoretical calculation and to provideoperating safety margins tone may operate the reactor at pressures fromabout 100 MPa to about 350 MPa, or from about 150 MPa to about 325 MPa,or from about 200 MPa to about 300 MPa, so that during the initialconversion of ethylene to polyethylene of up to about 10 weight %, or upto about 8 weight %, or up to about 7 weight % of polyethylene thereaction temperature is maintained above about 125 to about 135° C., orabove about 130° C., or above about 128° C.

Generally the initiator, or mixture of initiators, is injected into thereactor in amounts from about 100 to about 500 ppm, or from about 125 toabout 425, (based on the weight of the reactants). The initiator(s) maybe selected from oxygen, peroxides, persulphates, perborates,percarbonates, nitriles, and sulphides (methyl vinyl sulphide). Somefree radical initiators can be selected from the list given in Ehrlich,P., et al., Fundamentals of the Free-Radical Polymerization of Ethylene,Advances in Polymer Science, Vol. 7, pp. 386-448, (1970).

Non-limiting examples of some free radical producing substances includeoxygen (air); peroxide compounds such as hydrogen peroxide, decanoylperoxide, t-butyl peroxy neodecanoate, t-butyl peroxypivalate,3,5,5-trimethyl hexanoyl peroxide, diethyl peroxide, t-butylperoxy-2-ethyl hexanoate, t-butyl peroxy isobutyrate, benzoyl peroxide,t-butyl peroxy acetate, t-butyl peroxy benzoate, di-t-butyl peroxide,and 1,1,3,3-tetramethyl butyl hydroperoxide; alkali metal persulfates,perborates and percarbonates; and azo compounds such as azo bisisobutyronitrite. n one embodiment, initiators are selected from oxygen(air) and organic peroxides.

A chain transfer agent (sometimes referred to as a telogen or amodifier) may also be present in the reactants. The chain transfer agentmay be added at one or more points along the tubular reactor. Some chaintransfer agents include the saturated aliphatic aldehydes, such asformaldehyde, acetaldehyde and the like, the saturated aliphaticketones, such as acetone, diethyl ketone, diamyl ketone, and the like,the saturated aliphatic alcohols, such as methanol, ethanol, propanol,and the like, paraffins or cycloparaffins such as pentane, hexane,cyclohexane, and the like, aromatic compounds such as toluene,diethylbenzene, xylene, and the like, and other compounds which act aschain terminating agents such as carbon tetrachloride, chloroform, etc.

The chain transfer agent may be used in amounts from about 0.20 to about2, or from about 0.24 to about 1 mole percent based on the totalethylene feed to the reactor.

Phase diagrams for the liquid-liquid phase separation of monodispersepolyethylene and supercritical ethylene are known, at the temperatureand pressures ranges for a low density polyethylene reactor, however asfar as Applicant is aware there has been no recognition of the effectson reactor operation of liquid-liquid phase separation to form dropletsof high molecular weight polymer below the critical polymerconcentration. The problem is to determine the liquid-liquid equilibriumboundary and optionally the critical polymer concentration as a functionof the molecular weight distribution of the polymer.

Suitable equation of state models include lattice-fluid models such asFlory-Huggins and the Sanchez-Lacombe equation of state (Lacombe R. H.;Sanchez, I. C. Statistical Thermodynamics of Fluid Mixtures. J. Phys.Chem. 1976, 80 (23), 2568-2580; Sanchez, I. C.; Lacombe, R. H.Statistical thermodynamics of polymer solutions. Macromolecules 1978, 11(6), 1145-1156), as well as models based on thermodynamic perturbationtheory, for example, the perturbed chain statistical associating fluidtheory equation of state (Gross, J.; Sadowski, G, Perturbed-Chain SAFT:An Equation of State Based on a Perturbation Theory for Chain Molecules,Ind. Eng. Chem. Res., 2001, 40, 1244). Variants of that model (e.g.SAFT-VR, SAFT-LJ, soft-SAFT, SW-PC-SAFT, CK-PC-SAFT, or GC-SAFT-VR), orTPT1 and variations on this more general approach, such as TPT1-MSA andTPT1-RHNC may also be appropriate, as would thermodynamic perturbationtheories involving higher-than-first-order terms. Augmented cubicequations of state such as the Polymer-Soave-Redlich-Kwong equation ofstate (Hasan Orbey; Costas P. Bokis; Chau-Chyun Chen, Equation of StateModeling of Phase Equilibrium in the Low-Density Polyethylene Process:The Sanchez-Lacombe, Statistical Associating Fluid Theory, andPolymer-Soave-Redlich-Kwong Equations of State, Ind. Eng. Chem. Res.,1998, 37(11), pp 4481-4491) may have similar utility.

The Sanchez-Lacombe equation of state has been well known for at least20 years to those skilled in the art. This equation has the form

$\begin{matrix}{\frac{P}{RT} = {\frac{( {1 - d} )}{( {v + c} )} - {\frac{d^{2}}{b}{\ln( \frac{v + c - {b/d}}{v + c} )}} - \frac{a}{{{RT}( {v + c} )}^{2}}}} & (1)\end{matrix}$where T is the temperature, P is the pressure, R is the ideal gasconstant, ν is the molar volume, and a,b,c,d are mixture parameters. Themixture parameters are given by the following mixing rules

$\begin{matrix}{a = {\sum\limits_{i = 1}^{n_{c}}{\sum\limits_{j = 1}^{n_{c}}{x_{i}x_{j}d_{i}d_{j}v_{ij}{ɛ_{ij}( {1 - k_{ij}} )}}}}} & (2)\end{matrix}$where x_(i) is the mole fraction of component i and there are n_(c)components. The binary interaction parameter, k_(ij), is dependent ontemperature, k_(ij)=k_(ij) ^(a)+k_(ij) ^(b)T and d_(i) is a purecompound parameter related to the number of lattice sites occupied by amolecule. It is a linear function of molecular weight and is oftenexpressed as

$\frac{d_{i}}{M_{i}}$where M_(i) is the molecular weight. The cross parameters are given by

$\begin{matrix}{v_{ij} = \frac{( {v_{ii} + v_{jj}} )}{2}} & (3)\end{matrix}$where ν_(ii) is a pure compound parameter related to the size of alattice site, andε_(ij)=√{square root over (ε_(ii)ε_(jj))}  (4)where ε_(ii) is a pure compound lattice energy parameter. The bparameter is calculated as

$\begin{matrix}{b = {\sum\limits_{i = 1}^{n_{c}}{\sum\limits_{j = 1}^{n_{c}}{x_{i}x_{j}d_{i}d_{j}v_{ij}}}}} & (5)\end{matrix}$while the d parameter is

$\begin{matrix}{d = {\sum\limits_{i = 1}^{n_{c}}{x_{i}d_{i}}}} & (6)\end{matrix}$

The volume shift parameter is introduced to give better densitypredictions

$\begin{matrix}{c = {\sum\limits_{i = 1}^{n_{c}}{x_{i}c_{i}}}} & (7)\end{matrix}$

Polymer components are polydisperse, with a molecular weightdistribution (MWD) curve characterized using Size ExclusionChromatography (SEC). The MWD distribution curve can be converted to aset of i pseudocomponents with weight fractions w_(i) using therelationship:

$\begin{matrix}{w_{i} = {\int_{\log\; M_{i - 1}}^{\log\; M_{i}}{\frac{\mathbb{d}{WF}}{{\mathbb{d}\log}\; M}\ {\mathbb{d}\log}\; M}}} & (8)\end{matrix}$

The number-average molecular weight of the pseudocomponent M _(Ni) isdetermined using the expression:

$\begin{matrix}{{\overset{\_}{M}}_{Ni} = \frac{w_{i}}{\int_{\log\; M_{i - 1}}^{\log\; M_{i}}{\frac{1}{10^{\log\; M_{i}}}\frac{\mathbb{d}{WF}}{{\mathbb{d}\log}\; M}\ {\mathbb{d}M}}}} & (9)\end{matrix}$

For polydisperse polymers, the SEC data were converted to a set of 100pseudocomponents using equations (8) and (9). The integrations in theseequations were performed using the TableCurve 2D™ software. Thepseudocomponents are then used in phase equilibrium calculations usingVLXE software (VLXE ApS, Copenhagen, Denmark).

For application of this equation of state to this system, the parameterswere regressed based on a compromise between two sets of experimentaldata. The first data set was obtained from Chan and co-workers (Chan, A.K. C.; Adidharma, H.; Radosz, M., Fluid-Liquid Transitions ofPoly(ethylene-co-octene-1) in Supercritical ethylene Solutions, Ind.Eng. Chem. Res. 2000, 39, 4370. These data are significant because thepolymer is close to being monodisperse with a molecular weight of32,000. A second data set was Trumpi, H.; de Loos, Th. W.; Krenz, R. A.;Heidemann, R. A., High Pressure Phase Equilibria in the System LinearLow Density Polyethylene+Ethylene: Experimental results and Modeling.,J. Supercritical Fluids, 2003, 27(2), 205. These data are for a polymerhaving a molecular weight distribution which may be represented by 7pseudocomponents.

The results of the parameter regression are described in Table 1.

TABLE 1 Values of parameters used in the Sanchez-Lacombe equation ofstate Parameter Polyethylene Ethylene Lattice energy parameter, ε_(ii),K 495.2 275.24 Volume occupied per lattice site, 8.9838 7.4714 v_(ii)cm³/mol${{Number}\mspace{14mu}{of}\mspace{14mu}{lattice}\mspace{14mu}{sites}\mspace{14mu}{occupied}},\frac{d_{i}}{M_{i}}$0.06989 0.22713${{Volume}\mspace{14mu}{shift}\mspace{14mu}{parameter}},\frac{c_{i}}{M_{i}},{{mol}\text{/}g}$−0.4658 Binary interaction parameter k_(ij)(T) = 0.00904 − 0.0002892T(K)

The Sanchez-Lacombe equation of state, with the parameters in Table 1,was applied to the polyethylene/supercritical ethylene system. FIG. 1illustrates the predicted effect of molecular weight of a monodispersepolymer on the location of the cloud point curve at 210 MPa. Themolecular weight was varied from a low value of 5000 to a high value of5,000,000. The figure indicates that increasing the molecular weightincreases the size of the two-phase region of the phase diagram. Atemperature of at least about 115° C. may be used to keep an about5,000,000 molecular weight polymer in single phase at all compositions;this drops to about 100° C. for a molecular weight of about 100,000 andto about 70° C. for a molecular weight of about 10,000.

The Sanchez-Lacombe equation of state was also applied to polydispersepolymers in supercritical ethylene. Phase boundary calculations wereperformed for four different commercial grades of low densitypolyethylene, with melt index in the range of about 0.25 to about 25.The particular focus was on the about 0.25 melt index grade, since thisproduct was known to have a higher propensity for reactor fouling.

FIG. 2 is a calculated plot of the isobaric liquid-liquid phaseboundaries for the four commercial polyethylenes. LFY320C resin has thehighest cloud point temperature, as expected, because it has the highestproportion of high molecular weight material. A temperature of about110° C. is sufficient to keep this polymer from phase separating, andthe critical polymer concentration for this product is approximately 7wt %. The cloud point curves for the other resins are lower intemperature compared to LFY320C, and decrease monotonically with meltindex.

FIG. 3 is a calculated plot of the isobaric liquid-liquid phaseboundaries for the LFY320C resin as a function of pressure. The phaseboundary shifts to lower temperatures as the pressure is increased,indicating that the solvent quality of supercritical ethylene improveswith pressure.

Flash calculations were also performed to examine the composition of thephases formed below the liquid liquid phase boundary. FIG. 4 is acalculated plot of the isobaric cloud point curve overlaid with a curveshowing the magnitude of the weight-average molecular weight of polymerin the new phase formed at the cloud point for commercial polyethyleneLFY320C, based on the Sanchez-Lacombe equation of state. Initialsolutions whose polymer concentration is less than the critical valueyield new phases with polymer of higher molecular weight than the parentphase, and can have weight average molecular weights of about 500,000and above. It also shows that solutions whose polymer concentration islarger than the critical yield new phases of low molecular weight.

The phase equilibrium calculations described above indicate that phaseseparation of polymer solutions whose concentration is below thecritical value will yield a new liquid phase containing polymer of veryhigh molecular weight. For pressures similar to those in the reactor,this phase separation will occur at temperatures near about 100° C.,depending on the polymer concentration and molecular weightdistribution. There are no measurements of the crystallizationtemperature of polyethylene in ethylene solutions. The likely reason forthis is that cooling solutions of polyethylene will initially result inliquid-liquid phase separation and this can mask the detection of thesolid-liquid boundary (since crystallization measurements at very highpressure are usually made by observing the cloudiness of the solution ascrystals are formed, similar to the formation of the liquid-liquidsystem). As the system is cooled below the cloud point, the phasecontaining the higher molecular weight polymer/gel and higher polymerconcentration will eventually precipitate to yield semi crystallinepolymer.

Since there are no data for polymer crystallizing in ethylene solutions,it is useful to look at data for the crystallization of polymer in otherhydrocarbon solvents. FIG. 5 shows the crystallization phase boundary ofsolutions of polyethylene in isohexane under shear. Solutions of thesepolydisperse polyethylene samples crystallize at temperatures aboveabout 100° C., and the change in molecular weight from about 162,500 toabout 305,200 increases the crystallization temperature by about ˜10° C.This suggests that in a tubular LDPE reactor, the disperse liquid phasecontaining extremely high molecular weight gel have a crystallizationtemperature of the order of about 110° C. or more. This is consistentwith observations on reactor tubes that have been removed from service,which can have a high molecular weight polyethylene coating on the innerwall.

In the last few years, a more popular equation of state (EOS) formodeling high pressure polymer solutions has been the StatisticalAssociating Fluid Theory (SAFT) EOS (Chapman, W. G.; Gubbins, K. E.;Jackson, G.; Radosz, M. New Reference Equation of State for AssociatingLiquids. Ind. Eng. Chem. Res. 1990, 29, 1709. Huang, S. H.; Radosz, M.Equation of State for Small, Large, Polydisperse, and AssociatingMolecules. Ind. Eng. Chem. Res. 1990, 29, 2284. Huang, S. H.; Radosz, M.Equation of State for Small, Large, Polydisperse and AssociatingMolecules: Extensions to Fluid Mixtures. Ind. Eng. Chem. Res. 1991, 30,1994. Erich A. Müller; Keith E. Gubbins, Molecular-Based Equations ofState for Associating Fluids: A Review of SAFT and Related Approaches,Ind. Eng. Chem. Res., 2001, 40, 2193.). The Perturbed-Chain SAFT EOS isan improved form of the original SAFT EOS.

The PC-SAFT EOS, molecules are conceived as chains composed of sphericalsegments, as shown in FIG. 6. In FIG. 6 the arrows are representative ofthe interaction between N-alkane (CH₂) segments. The interactions arebased on the average radial distribution function betweenindistinguishable segments on one chain with those on another. Theintermolecular potential energy function describing the interactionbetween segments, which distinguishes PC-SAFT from SAFT, is given by themodified square-well potential suggested by Chen and Kreglewski(Applications of the Augmented van der Waals Theory of Fluids. I. PureFluids. Ber. Bunsen-Ges. Phys. Chem., 1977, 81, 1048-1052) and isillustrated in FIG. 7.

In this figure, the circle represents a spherical segment of a moleculechain, the bold line represents the intermolecular potential energy,u(r) (in J) is the inter-segment potential energy function, r (in Å) isthe radial distance from the middle of a segment, σ (in Å) is thetemperature-independent segment diameter, ε (in J) the depth of thepotential energy well, and λ the reduced square-well width, with s₁being fixed at 0.12σ. The ‘step’ in the potential energy function (thestep from 3ε to −ε) accounts for an essential feature of real moleculebehavior, namely soft repulsion. Based on this picture, molecules ofeach pure compound are characterized by three pure compound parameters:the temperature-independent segment diameter, σ (Å); the depth of thepotential energy well ε (J); and the number of segments in each chain,m. The number of segments in the chain relates to the molecular weight.

In the original SAFT EOS, the Helmholtz energy of the reference fluid,A^(hc), which is a chain of bonded hard spheres was obtained as a sum ofterms accounting for the repulsive energy of non-interacting hardspheres, A^(hs), the energy of forming chains from these spheres throughcovalent bonding, A^(cf), and the energy of forming clusters(association) via, say, hydrogen bonding, A^(ass), i.e.A ^(hc) =A ^(hs) +A ^(cf) +A ^(ass)  (10)

The PC-SAFT EOS uses the same terms. However, the systems examined inthis study do not exhibit association and this term is set to zero, sothat for the PC-SAFT EOS:A ^(hc) =A ^(hs) +A ^(cf)  (11)

Returning to equation (10), in the PC-SAFT EOS, the Boublik (Boublik, T.Hard-Sphere Equation of State. J. Chem. Phys. 1970, 53, 471) andMansoori et al (Mansoori, G. A.; Carnahan, N. F.; Starling, K. E.;Leland, T. W. Equilibrium Thermodynamic Properties of the Mixture ofHard Spheres. J. Chem. Phys. 1971, 54, 1523) expression for theHelmholtz energy of a mixture of monomeric non-attracting hard spheresegments is used:

$\begin{matrix}\begin{matrix}{\frac{A^{hs}}{n_{t}{RT}} = {\overset{\_}{m}\;{\overset{\sim}{a}}^{hs}}} \\{= {\frac{\overset{\_}{m}}{\zeta_{0}} \cdot \lbrack {\frac{3\zeta_{1}\zeta_{2}}{( {1 - \zeta_{3}} )} + \frac{\zeta_{2}^{3}}{{\zeta_{3}( {1 - \zeta_{3}} )}^{2}} + {( {\frac{\zeta_{2}^{3}}{\zeta_{3}^{2}} - \zeta_{0}} ) \cdot {\ln( {1 - \zeta_{3}} )}}} \rbrack}}\end{matrix} & (12)\end{matrix}$where ã^(hs) is the reduced molar Helmholtz energy of hard spheremonomers, per mole of segments [hence the factor m in equation (12)].The average number of segments in the solution is

${\overset{\_}{m} = {\sum\limits_{i}{x_{i}m_{i}}}},$with

$\begin{matrix}{\zeta_{n} = {{\frac{\pi}{6}\rho{\sum\limits_{i = 1}^{N_{c}}\;{x_{i}m_{i}d_{i}^{n}\mspace{31mu} n}}} \in \{ {0,1,2,3} \}}} & (13)\end{matrix}$m_(i) is the number of segments in a chain of component i and d_(i) (Å)is the temperature dependent diameter of the monomeric hard spheresegments (Chen and Kreglewski, 1977):

$\begin{matrix}{{d_{i}(T)} = {\sigma_{i} \cdot ( {1 - {0.12 \cdot {\exp( {- \frac{3 \cdot ɛ_{i}}{kT}} )}}} )}} & (14)\end{matrix}$which is a function of the previously described temperature-independentparameters σ_(i) (Å) and (ε/k)_(i) (K) for component i. The packingfraction, ζ₃=η, is the ratio of the volume occupied by the segments tothe total volume available.

The chain formation Helmholtz energy term in equation (10), used in theSAFT EOS, is described by Chapman et al (1990). This accounts for thechange in Helmholtz energy due to creating covalent bonds from monomericspherical segments and has the following form:

$\begin{matrix}{\frac{A^{cf}}{n_{t}{RT}} = {{\overset{\sim}{a}}^{cf} = {\sum\limits_{i = 1}^{N_{c}}\;{{x_{i}( {1 - m_{i}} )}\rho\;{\ln\lbrack {g_{ii}^{hs}( \sigma_{ii} )} \rbrack}}}}} & (15)\end{matrix}$where ã^(cf) is the reduced molar Helmholtz energy of chain formation,per mole of chains and g_(ii) ^(hs)(σ_(ii)) is the hard sphere paircorrelation (or radial distribution) function for the interaction of twospheres i and j in a mixture of spheres, evaluated at the hard spherecontact distance, σ_(ij):

$\begin{matrix}{{g_{ij}^{hs}( \sigma_{ij} )} = {\frac{1}{( {1 - \zeta_{3}} )} + {( \frac{d_{i}d_{j}}{d_{i} + d_{j}} )\frac{3\zeta_{2}}{( {1 - \zeta_{3}} )^{2}}} + {( \frac{d_{i}d_{j}}{d_{i} + d_{j}} )^{2}\frac{2\zeta_{2}^{2}}{( {1 - \zeta_{3}} )^{3}}}}} & (16)\end{matrix}$

Equations (11), (12) and (15) are used to calculate A^(hc) in PC-SAFTEOS.

The total Helmholtz energy of the system, A, is given by:A=A ^(id) +A ^(hc) +A ^(pert)  (17)where A^(id), A^(hc), and A^(pert) are the ideal gas, hard sphere chainand perturbation contributions to the Helmholtz energy. The ideal gascontribution to the Helmholtz energy A^(id) has the following form, fora system of Nc components with mole fractions x_(i):

$\begin{matrix}{\frac{A^{id}}{n_{t}{RT}} = {{\overset{\sim}{a}}^{id} = {{\sum\limits_{i = 1}^{N_{c}}\;{x_{i}{\ln( {\rho_{i}\Lambda_{i}^{3}} )}}} - 1}}} & (18)\end{matrix}$where ã^(id) is the reduced ideal gas Helmholtz energy per mole ofchains,

${\rho_{i} = \frac{N_{i}}{V}},$the number density of component i where N_(i) is the number of chains ofcomponent i and V is the total volume available. The temperature is T,n_(t) the total number of moles, Λ_(i) the de Broglie wavelength ofcomponent i and R is the Ideal Gas constant. The de Broglie wavelengthof component i with chains of mass m_(pi) is given by:

$\begin{matrix}{\Lambda_{i} = \sqrt{\frac{2\pi\; m_{pi}{kT}}{h^{2}}}} & (19)\end{matrix}$Where h is Planck's constant and k is Boltzmann's constant. Thisexpression yields a compressibility factor equal to 1 upondifferentiation, as expected for an ideal gas.

The last term in the Helmholtz energy, equation (17), A^(pert), arisesfrom attractive ‘dispersion’ interactions and distinguishes the PC-SAFTEOS from the original SAFT EOS. In most thermodynamic perturbationtheories (Boublik, T.; Perturbation Theory, Chapter 2 in Equations ofState for Fluids and Fluid Mixtures Part 1, Sengers, J. V.; Kayser, R.F.; Peters, C. J.; White, H. J.; (eds.), 2000, Elsevier Science, N.Y.),it is equated directly to the dispersion energy, i.e.,A^(pert)=A^(disp). In the original SAFT EOS, the perturbationcontribution is based on the dispersion energy due to interactionsbetween isolated spheres, adjusted to reflect the real behaviour ofargon (Chen and Kreglewski, 1977), but PC-SAFT is based on multi-spherebonded chains, in the form of the homologous series of n-alkanes (n-C₁to n-C₃₀). In the PC-SAFT EOS, this perturbation contribution isobtained from Barker and Henderson's (Barker, J. A.; Henderson, D.;Perturbation Theory and. Equation of State for Fluids. II. A SuccessfulTheory for Liquids. J. Chem. Phys., 1967, 47, 4714-4721) 2nd orderperturbation theory as a sum of first (A₁) and second (A₂) orderperturbation terms:

$\begin{matrix}{\frac{A^{pert}}{n_{t}{RT}} = {\frac{A^{disp}}{n_{t}{RT}} = {{\overset{\sim}{a}}^{disp} \cong {\frac{A_{1}}{n_{t}{RT}} + \frac{A_{2}}{n_{t}{RT}}}}}} & (20)\end{matrix}$where ã^(disp) is the residual Helmholtz energy due to dispersionforces, per mole of chains. Gross and Sadowski (2001) applied Barker andHenderson's theory to a system of chain molecules interacting via asquare-well potential using Chiew's (1991) expression for the radialdistribution function of interacting hard chains. They approximated theresulting two integrals of the radial distribution function in A₁ and A₂using a temperature-independent power series ranging to 6th order inpacking fraction (η) and dependent on the average number of segments inthe molecule (m). For a mixture, the integral in A₁ is given by theexpression

$\begin{matrix}{{I_{1}( {\eta,\overset{\_}{m}} )} = {{\int_{1}^{\infty}{{\overset{\sim}{u}(x)}{g^{hc}( {\overset{\_}{m};{x \cdot \frac{\sigma}{d}}} )}x^{2}\ {\mathbb{d}x}}} = {\sum\limits_{i = 1}^{6}\;{{a_{i}( \overset{\_}{m} )}\eta^{i}}}}} & (21)\end{matrix}$with the function a_(i)(m) given by

$\begin{matrix}{{a_{i}( \overset{\_}{m} )} = {a_{0\; i} + {\frac{\overset{\_}{m} - 1}{\overset{\_}{m}}a_{1\; i}} + {\frac{\overset{\_}{m} - 1}{\overset{\_}{m}}\frac{\overset{\_}{m} - 2}{\overset{\_}{m}}a_{2\; i}}}} & (22)\end{matrix}$where {a_(0i),a_(1i),a_(2i), 1≦i≦6} are adjustable constants. Theintegral in A₂ is represented by a similar function:

$\begin{matrix}{{I_{2}( {\eta,\overset{\_}{m}} )} = {{\frac{\partial}{\partial\rho}\lbrack {\rho{\int_{1}^{\infty}{( {\overset{\sim}{u}(x)} )^{2}{g^{hc}( {\overset{\_}{m};{x \cdot \frac{\sigma}{d}}} )}x^{2}\ {\mathbb{d}x}}}} \rbrack} = {\sum\limits_{i = 1}^{6}\;{{b_{i}( \overset{\_}{m} )}\eta^{i}}}}} & (23)\end{matrix}$with the function b_(i)(m) being given by:

$\begin{matrix}{{b_{i}( \overset{\_}{m} )} = {b_{0\; i} + {\frac{\overset{\_}{m} - 1}{\overset{\_}{m}}b_{1\; i}} + {\frac{\overset{\_}{m} - 1}{\overset{\_}{m}}\frac{\overset{\_}{m} - 2}{\overset{\_}{m}}b_{2\; i}}}} & (24)\end{matrix}$where {b_(0i),b_(1i),b_(2i), 1≦i≦6} are adjustable constants. Theconstants in equations (22) and (24) were determined by fitting purecomponent data for n-alkanes. First the integrals were fully evaluatedfor Lennard-Jones (LJ) chains, using the expressions in the note aboveand an averaged radial distribution function for segments in LJ chains,and n-alkane vapour pressure and density data were regressed to obtainthe values of three pure compound parameters m, σ and ε/k (the segmentnumber, segment diameter and reduced interaction energy magnitude, wherek (J/K) is Boltzmann's constant). Once this was done, the constants inthe polynomial expressions for the integrals were evaluated forn-alkanes, from methane to triacontane, using vapour pressure, liquid,vapour and supercritical density data. Hence, the PC-SAFT equationreproduces n-alkane data accurately. Optimal values of the adjustableconstants {a_(0i),a_(1i),a_(2i),b_(0i), b_(1i),b_(2i), 1≦i<6} are listedbelow

Values of Universal Constants in the PC-SAFT EOS l a_(0i) a_(1i) a_(2i)b_(0i) b_(1i) b_(2i) 0 0.9105631445 −0.3084016918 −0.09061483510.7240946941 −0.5755498075 0.0976883116 1 0.6361281449 0.18605311590.4527842806 2.2382791861 0.6995095521 −0.2557574982 2 2.6861347891−2.5030047259 0.5962700728 −4.0025849485 3.8925673390 −9.1558561530 3−26.547362491 21.419793629 −1.7241829131 −21.003576815 −17.21547164820.642075974 4 97.759208784 −65.255885330 −4.1302112531 26.855641363192.67226447 −38.804430052 5 −159.59154087 83.318680481 13.776631870206.55133841 −161.82646165 93.626774077 6 91.297774084 −33.746922930−8.6728470368 −355.60235612 −165.20769346 −29.666905585

For application to other fluids, the constants in the expressions forthe integrals are set to the values optimized for n-alkanes, and henceare assumed to be universal for all compounds. The values of the threepure compound parameters; the segment number, m, the segment diameter,σ, and the reduced interaction energy, ε/k are then fit to pure compounddata for the compound of interest. The EOS was extended to mixturesusing the usual one fluid mixing rules incorporating a binaryinteraction parameter k_(ij) to correct the segment-segment interactionenergies of unlike chains. Hence the final form of the Helmholtz energyis:

with

$\begin{matrix}{{\overset{\sim}{a}}^{disp} = {\frac{A_{1}}{n_{t}{RT}} + \frac{A_{2}}{n_{t}{RT}}}} & (25) \\{\frac{A_{1}}{n_{t}{RT}} = {{- 2}{\pi\rho}\;{I_{1}( {\eta,\overset{\_}{m}} )}\overset{\_}{m^{2}{ɛ\sigma}^{3}}}} & (26)\end{matrix}$and a one-fluid quadratic mixing rule for the segment diameter andenergy-well parameter

$\begin{matrix}{\overset{\_}{m^{2}{ɛ\sigma}^{3}} = {\sum\limits_{i = 1}^{N_{C}}\;{\sum\limits_{j = 1}^{N_{c}}\;{x_{i}x_{j}m_{i}{m_{j}( \frac{ɛ_{ij}}{kT} )}\sigma_{ij}^{3}}}}} & (27)\end{matrix}$

The mixture segment diameter between pairs of segments is calculated asan arithmetic average

$\begin{matrix}{\sigma_{ij} = {\frac{1}{2}( {\sigma_{i} + \sigma_{j}} )}} & (28)\end{matrix}$while the mixture potential well-depth of FIG. 2 is obtained fromgeometric averaging, with a binary interaction parameter to correct forasymmetry:ε_(ij)=√{square root over (ε_(i)ε_(j))}·(1−k _(ij))  (29)

As usual, the value of the binary interaction parameter k_(ij) isobtained by fitting phase equilibrium data.

The same experimental data was used to fit the system-dependentparameters to the PC-SAFT equation of state, those of Chun Chan et al.(2000) and Trumpi et al. (2003).

When the solving equations of state using the data developed using theabove methods the calculations fit the actual measured data at each ofthe data points but was less than desirable between the data points.Hence, a decision was made to regress new values of the liquid liquidparameters ε_(ii) and binary interaction parameters k_(ij) ^(a) andk_(ij) ^(b). The EOS parameters were fit to the data to provide a goodcompromise between the two sets of data.

It was found that using the regressed values in the liquid liquidequation of state and breaking a polymer's molecular weight distributioninto a set of pseudocomponents at least about 80, or about 100, or about120 or greater) provided a good fit with the physical properties of thepolymer.

FIG. 8 illustrates the liquid-liquid phase boundary calculated formonodisperse polyethylene in supercritical ethylene at about 210 MPa,using the PC-SAFT equation of state. The results obtained with thismodel are similar to those obtained with the Sanchez-Lacombe equation ofstate.

One further advantage of an embodiment of the present invention is thatit provides a method to closely approximate the equations of state for apolyethylene polymer for which there is a molecular weight distributioncurve (e.g. SEC graph).

The present invention has been described with reference to certaindetails of particular embodiments thereof. It is not intended that suchdetails be regarded as limitations upon the scope of the inventionexcept insofar as and to the extent that they are included in theaccompanying claims.

What is claimed is:
 1. A method to determine the curve of the liquidliquid equilibrium boundary as a function of molecular weightdistribution (MWD) for a multitude of different products comprising fromabout 80 to about 100 wt. % of ethylene and about 0 up to about 20weight % of one or more C₃₋₈ alpha olefins having a molecular weightfrom about 8,000 to about 500,000 produced in super critical ethylene ina high pressure reactor at temperatures from about 80° C. to about 350°C. and pressures from about 100 MPa to about 350 MPa comprising: a)modeling experimental or literature data for the liquid liquidequilibrium using an equation of state model to describe the effects ofthe molecular weight and the polydispersity of the polyethylene on theliquid liquid equilibrium curve b) determining the composition-specificparameters of the model from a); and, c) applying an equation of stateselected from PC-SAFT, SAFT-VR, SAFT-LJ, soft SAFT, SW-PC-SAFT,CK-PC-SAFT, and GC-SAFT-VR to the temperature, pressure and compositionconditions of the reaction to generate the liquid liquid equilibriumboundary and optionally the critical polymer concentration.
 2. Theprocess according to claim 1 wherein the reactor is a tubular reactor.3. A process to prepare a liquid polymer lean/liquid polymer rich andliquid liquid phase diagram for a reactor for polymerizing a systemcomprising a polymer having a weight average molecular weight from about8,000 to about 500,000 comprising from about 80 to about 100 wt % ofethylene and about 0 to about 20 wt % of one or more C₃₋₈ alpha olefinsin super critical liquid ethylene at temperatures from about 80° C. toabout 350° C. and pressures from about 100 MPa to about 350 MPa todefine operating conditions at which the polymer is substantiallydissolved in the liquid phase comprising: preparing a phase diagram forliquid polymer lean/liquid polymer rich for said reactor and process attemperatures from about 150° C. to about 350° C. and pressures fromabout 100 to about 350 MPa; b) inserting into said phase diagram aliquid liquid phase boundary determined according to claim
 1. 4. Amethod for conducting the polymerization of a polymer having a weightaverage molecular weight from about 8,000 to about 500,000 comprisingabout 80 to about 100 wt % of ethylene and about 0 to about 20 wt. % ofone or more C₃₋₈ alpha olefins in super critical liquid ethylene attemperatures from about 80° C. to about 350° C. and pressures from about100 MPa to about 350 MPa to define operating conditions at which thepolymer is substantially dissolved in the liquid phase Comprisingmonitoring the heat balance of said reaction and determining when thereis an apparent loss of cooling and comparing the operating conditions tothe phase diagram according to claim 3, and adjusting one or more of thetemperature and pressure conditions to bring the operating conditionsmore than about 5% more within the liquid area of the phase diagram. 5.The method according to claim 4, wherein the operating conditions areadjusted to bring them within the liquid area of the phase diagram bymore than about 10%.
 6. The method according to claim 5, wherein thephase diagram is digitized and stored on a microprocessor and heatbalance for the reaction is monitored using a microprocessor and theoperating conditions are adjusted using a microprocessor.
 7. A method toextend the run time between cleanings of a high pressures reactor forthe polymerization of a polymer having a weight average molecular weightfrom about 8,000 to about 500,000 comprising about 80 to about 100 wt %of ethylene and about 0 to about 20 wt % of one or more C₃₋₈ alphaolefins in super critical ethylene at temperatures from about 80° C. toabout 350° C. and pressures from about 100 MPa to about 350 MPacomprising operating according to claim 5, so that not more than about30 minutes elapse between the apparent loss of cooling and achieving thenew operating conditions within the liquid area within the phasediagram.
 8. The method according to claim 7, wherein the time to achievethe adjusted operating conditions is less than about 15 minutes.
 9. Amethod to dissolve precipitated polymer in a high pressures reactor forthe polymerization of a polymer having a weight average molecular weightfrom about 8,000 to about 500,000 comprising about 80 to about 100 wt %of ethylene and about 0 to about 20 wt % of one or more C₃₋₈ alphaolefins in super critical liquid ethylene at temperatures from about 80°C. to about 350° C. and pressures from about 100 MPa to about 350 MPacomprising operating according to claim 7, so that not more than about30 minutes elapse between the apparent loss of cooling and achieving thenew operating conditions within the liquid area within the phasediagram.
 10. The method according to claim 9, wherein the phase diagramis digitized and stored on a microprocessor and heat balance for thereaction is monitored using a microprocessor and the operatingconditions are adjusted using a microprocessor.
 11. The method accordingto claim 10 wherein the time to achieve the adjusted operatingconditions is less than about 15 minutes.